基于无单元局部弱式法的2.5维直流电阻率正演  

2.5D DC resistivity forward modeling based on a local weak form element⁃free method

作　　者：麻昌英 闫玲玲 姚振岸 柳建新[2] 赵文学 周聪[1,3] MA Changying;YAN Lingling;YAO Zhen’an;LIU Jianxin;ZHAO Wenxue;ZHOU Cong(Engineering Research Center for Seismic Disaster Prevention and Engineering Geological Disaster Detection of Jiangxi Province,East China University of Technology,Nanchang,Jiangxi 330013,China;Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring(Central South University),Ministry of Education,Changsha,Hunan 410083,China;School of Geophysics and Measurement‑Control Technology,East China University of Technology,Nanchang,Jiangxi 330013,China)

机构地区：[1]江西省防震减灾与工程地质灾害探测工程研究中心(东华理工大学),江西南昌330013 [2]中南大学有色金属成矿预测与地质环境监测教育部重点实验室,湖南长沙410083 [3]东华理工大学地球物理与测控技术学院,江西南昌330013

出　　处：《石油地球物理勘探》2023年第4期1002-1016,共15页Oil Geophysical Prospecting

基　　金：国家自然科学基金项目“多源条件下复杂模型直流电阻率无单元伽略金法三维快速正演”(41904097);“黏弹各向异性介质复杂震源机制解析与微地震响应高精度正演”(42004113);“基于非结构有限元的频率域海洋CSEM和MT三维联合反演”(42274104);江西省自然科学基金项目“基于关键技术改进加速的直流电阻率无单元单位分解法三维正演”(20202BAB211011);“基于盲源分离的阵列大地电磁强干扰压制”(20202BABL211017)、有色金属成矿预测与地质环境监测教育部重点实验室(中南大学)开放基金资助项目“基于FEM扩边和支持域改进的直流电阻率无单元单位分解法2.5维快速正演”(2020YSJS05);江西省主要学科学术带头人培养计划项目“频率域电磁法三维快速正反演研究及统一平台建设”(20204BCJL23058)联合资助。

摘　　要：传统的数值模拟方法依赖于节点连接信息的单元,基于全局弱式的无单元Galerkin法虽然无需节点连接信息的单元剖分,但仍依赖于全局域内剖分的背景积分单元。文中基于无单元Galerkin法,利用单位分解积分法将全局域积分转化为节点局部域积分,从而不再需要全局域内剖分的背景积分单元,进一步减小了对单元的依赖,实现了更灵活和更高精度的2.5维直流电阻率无单元局部弱式法正演模拟。分别应用该算法、无单元Galerkin法及有限单元法对不同地电模型进行数值模拟及效果对比,证明了所提算法对直流电阻率正演模拟的正确性和有效性。相比于无单元Galerkin法和有限单元法,文中算法具有更强的灵活性和适应性、更高的精度。为了提高该算法对地形起伏模型的模拟精度,对地形起伏区域进行节点加密,并对地形以外的高斯点不做计算,可获得与无单元Galerkin法和有限单元法(FEM)基本一致的效果。The traditional numerical simulation method relies on elements based on nodal connection information,so its application is limited.Although the element‑free Galerkin method(EFGM)based on the global weak form does not require the division of elements based on nodal connection information,it still relies on the background quadrature elements divided in the global domain.In this paper,the partition of unity quadrature method is used to transform the global local integration into nodal local domain integration based on EFGM.Therefore,the background quadrature element divided in the global domain is not needed,and the dependence on the element is further reduced.As a result,2.5‑dimensional direct current(DC)resistivity forward modeling based on a local weak form elementfree method is realized with higher flexibility and accuracy.The proposed method,the EFGM,and the finite element method(FEM)are respectively used to simulate different geoelectric models,and the results are compared,which prove the correctness and effectiveness of the proposed method for the forward modeling of DC resistivity.In addition,the flexibility and adaptability of the proposed method are better than those of EFGM and FEM,with higher accuracy and low computational efficiency.In order to improve the accuracy of this method in simulating the undulating terrain,node encryption is carried out in the undulating terrain,and Gaussian points outside the terrain are not calculated.The results are basically consistent with those obtained by the EFGM and FEM.

关 键 词：无单元局部弱式法 有限单元法 单位分解积分 正演模拟 直流电阻率 

分 类 号：P631[天文地球—地质矿产勘探]